Imaging Schemes for Perfectly Conducting Cracks

We consider the problem of locating perfectly conducting cracks and estimating their geometric features from multi-static response matrix measurements at a single or multiple frequencies. A main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal-to-noise ratios. In this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength-to-crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks. A central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multi-static response matrix measurements. We present numerical experiments to illustrate some of our main findings. Key words. asymptotic imaging, crack detection, imaging algorithms, random matrices, measurement noise, hypothesis testing...

• Type: Journal
• Year: 2011
• Where: SIAMAM
• Authors: Habib Ammari, Josselin Garnier, Hyeonbae Kang, Won-Kwang Park, Knut Sølna
• Keywords: Crack Detection, Multi-static Response Matrix, Response Matrix Measurements, SIAMAM 2011, Software Engineering